Infinity is not a number.
There are different classes of infinity:
The sets of natural numbers, integers, rational numbers all belong to the smallest class, with a cardinality of Aleph-null.
The sets of Irrational Numbers and real numbers belong to the next higher level of infinity, with cardinality Aleph-One.
Infinity can give rise to a very large number of apparent paradoxes - infinitely many of them?
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Infinity... 5 over 0 will be represented as 5/0 Any number divided by 0 results in infinity
There are multiple ways to interpret this question-that is, you could mean either (5-x+cosx)/x or 5-x +(cosx/x). The limit of the second option is negative infinity because as x approaches infinity, |cosx/x|≤1, so 5-x+cosx/x is very close to 5-x, and 5-infinity is basically negative infinity. For the first option, we consider that -1≤cosx≤1. This implies that, as x approaches infinity, lim of (5-x-1)/x≤lim of (5-x+cosx)/x≤lim of (5-x+1)/x. Simplifying, we get that, as x approaches infinity, lim of (4-x)/x≤lim of (5-x+cosx)/x≤(6-x)/x. Simplifying our new limits, we get -1≤lim of (5-x+cosx)/x≤1. It is now clear that the limit of (5-x+cosx)/x as x approaches infinity =negative 1.
7
multiplication facts are simply that times table in this case 5
1 one infinity divided by infinity